The classification of a Hopf algebra whose dimension is three product of primes in general is also open. The study of Hopf algebras of dimension \(p^3\)  was carried out by García [1]} and he proved that the only ribbon Hopf algebras of dimension \(p^3\)  are group algebras and Frobenius-Lusztig kernels; The Hopf algebras with dimension \(2p^2\)  (\(p\)  is an odd prime) has been researched by several experts: Andruskiewitsch and Natale (see [2]}) classified all such non-semisimple pointed Hopf algebras, and Hilgemann-Ng (see [3]}) proved that if a Hopf algebra \(H\)  of dimension \(2p^2\)  is not semisimple, then \(H\)  or \(H^{\ast }\)  must be pointed. Cheng-Ng (see [4]}) considered Hopf algebras with dimension \(4p\)  and proved that every such non-semisimple Hopf algebra \(H\)  is pointed if and only if \(H\)  satisfies that \(|G(H)|>2\) . The non-simple and semisimple Hopf algebras of dimension \(pq^2\) , where \(p,q\)  are distinct primes, were classified in [5]}.
